International Journal of Research and Innovation (IJRI)
International Journal of Research and Innovation (IJRI) 1401-1402
INTERFACIAL STRESS ANALYSIS OF EXTERNALLY PLATED RC BEAMS
T.Haseena1, M.V.Seshagiri rao2, K. Mythili3 1 Research Scholar, Department Of Civil Engineering, Aurora Scientific Technological and Research Academy, Hyderabad India. 2 Professor, Department Of Civil Engineering, JNTU Hyderabad, Hyderabad, India 3 Associate professor , Department Of Civil Engineering, Aurora Scientific Technological and Research Academy, Hyderabad India.
Abstract Strengthening reinforced concrete (RC) beams by bonding steel or fibre reinforced polymer (FRP) on its tension face has become a popular retrofit method due to its rapid, simple and other advantages. However, debonding along the Steel-RC beam interface can lead to premature failure of the structures. The interfacial stresses play a significant role in understanding this premature debonding failure of such repaired structures. This paper presents a careful finite element investigation into interfacial stresses in the adhesive layer bonding RC beam and soffit plate. Finite element modelling issues like proper selection of contact between adherents and symmetry conditions are first discussed, with particular attention on appropriate finite element meshes for the accurate determination of interfacial stresses. The interfacial stress behaviour at plate end has been analysed for two cases of loading taken one by applying uniformly distributed load and the other with a two point loading. Two special cases are considered in two point loading – for the cases when the plate terminates with-in the constant moment region (CMR) and for the case when plate is extended beyond constant moment region where bending moment is minimal. The interfacial stresses are increasing with a reduction in adhesive layer thickness where as the stresses are increasing with the increase in soffit plate thickness. Carbon fibre reinforced polymer (CFRP) has shown a significant reduction in interfacial stresses when compared to steel plate. The interfacial stresses for the plate restricted within the constant moment region are very high near the plate end leading to flexural debonding compared to the case where plate is extended beyond constant moment region where bending moment is minimal. The concentration of stresses in the adhesive layer near the plate end explained the significance in considering their influence in flexural debonding. Keywords-- Interfacial stresses, flexural debonding, constant moment region, soffit plate, finite element method. *Corresponding Author:
T.Haseena, Research Scholar, Department Of Civil Engineering, Aurora Scientific Technological and Research Academy, Hyderabad India. Published: January 02, 2015 Review Type: peer reviewed Volume: II, Issue : I
Citation: T.Haseena, Research Scholar, (2014) "Interfacial Stress Analysis Of Externally Plated Rc Beams".
INTRODUCTION Reinforced concrete structures often have to face modification and improvement of their performance during their service life. The main contributing factors are change in their use, new design standards, lack of maintenance practices, deterioration due to corrosion caused by exposure to an aggressive environment and accident events such as earthquakes. In such circumstances there are two possible solutions: replacement or retrofitting. Full structure replacement might have determinate disadvantages such as high costs for material and labour, a stronger environmental impact and inconvenience due to interruption of the function of the structure e.G. Traffic problems. When possible it is often better to repair or upgrade the structure by retrofitting.
The strengthening of reinforced concrete beams by bonding a soffit plate has become a popular retrofit procedure .This plate bonding technique has numerous advantages such as increasing the stiffness and strength of an existing flexural member with minimal impact on the surrounding environment. Considerable research has been undertaken on rc beams strengthened with a bonded soffit plate. Tests on rc beams bonded with either steel plates or fibre reinforced plastic plates have revealed that debonding of the soffit plate from the rc beam, typically with the concrete cover attached to the plate, is a common failure mode in these beams. This debonding failure mode is brittle and prevents the full utilization of the tensile strength of the bonded plate. It is therefore important to understand the mechanism of this debonding failure mode and develop sound design rules. Debonding failures are majorly occurred due to high interfacial shear or normal stresses that are developed while transferring the tensile stresses from the bonded plate to the rc beam near the end of the plate. Accurate predictions of these interfacial stresses are thus the key to understand the debonding failure phenomenon and the starting point for developing accurate debonding strength models. Consequently, the determination of interfacial stresses has been researched for the last decade for beams bonded with either steel or frp plates. In particular, several closed-form analytical solutions 116
International Journal of Research and Innovation (IJRI)
have been developed.
Interaction
FINITE ELEMENT MODELLING
The full interaction between adherents can be assigned by using tie constraint. For creating tie constraint the concrete beam surface should be considered as master surface and the adhesive surface should be considered as slave surface. The slave surface should have finer mesh size than the master surface.
Geometric modelling of RC beam, Adhesive layer and soffit plate has been done separately using the part module. The material behaviour was assumed to be homogeneous and isotropic. The material properties such as elastic properties were assigned using the property module. Only a quarter model is prepared to analyze due to constraints in computational resources. The externally plated RC beam model is discretised into a mesh consisting of C3D8R element – An 8-node linear brick Element with Reduced integration. Each node has six degrees of freedom. Boundary condition Simply supported boundary condition is considered for the analysis. That is, one end of the RC beam attached with hinge and other end with roller. In hinged support, all the three displacements (U1=U2=U3=0) along x, y and z directions are arrested. In roller support, two displacements (U1=U2=0) along y and x directions are arrested and other one (U3=0) along z direction is free to move along its axis. Since, a quarter model is only formed symmetry conditions were given at all the necessary nodes in both x direction and z direction. This helps to make the model work like a complete structure. Loading conditions In the present study the plated rc beam is analysed under uniformly distributed loading condition and two- point loading condition. The load is applied along the span of the beam as pressure over the top surface for udl and two-point loading is given like total load on two extruded surfaces over the beam where loading has to be done. Three cases are considered and models are created accordingly. Case-1: externally plated rc beam subjected to uniformly distributed load. Case-2: externally plated rc beam subjected to twopoint loading with plate terminated within the constant moment region. Case-3: externally plated rc beam subjected to twoPoint loading with plate extended beyond the constant moment region to a point where bending moment is minimal.
VALIDATION In order to develop the finite element model, reference beam model is selected from literature and used J.G.Teng, J.W.Zhang, S.T.Smith (2001) have carried out a numerical investigation on the interfacial stresses in the adhesive layer through computational approach comparing with a closed form solution developed by Smith and Teng. The influence of various material and geometric properties on interfacial stresses has been studied. Poisson’s ratio
Component
Width, mm
Depth, mm
Length, mm
Youngs modulus, MPa
Concrete
100
150
2400
20000
0.17
Adhesive
100
4
1800
2000
0.25
Steel Plate
100
4
1800
200000
0.3
table.1. Material properties of adherents The geometric and the material properties of the beam model is taken for validation from their study. The boundary conditions adopted for the plated beam is simply supported. It is subjected to a uniformly distributed load of 15N/mm. The material properties of validating model are given in table.1.
Element type
Finite Element model for present study
Eight-node brick element with reduced integration (C3D8R) was used throughout in modelling all components of beam. The C3D8R element is a general purpose linear brick element, with reduced integration (1 integration point). Due to the reduced integration, the locking phenomena observed in the C3D8 element do not show in C3D8R.
The behaviour of interfacial stresses has been investigated by considering the effect of various geometric and mechanical properties of the adherents. Major two cases considered in the present study are the behaviour and influence of interfacial stresses near the plate end for the cause of failure when the beam is subjected to uniformly distributed load and two-point loading. Further, two cases are consid117
International Journal of Research and Innovation (IJRI)
ered in two-point loading, for the plate when terminated within the constant moment region and the plate extended beyond the constant moment region where the bending moment is minimal.
comprehensive assessment of the performance of the plated beams. The beam of Figure 3.6 was taken as the reference beam. The parameters varied in the present study include• The adhesive layer thickness •
The adhesive layer elastic modulus
•
The soffit plate thickness
•
The soffit plate material
Loading Two loading conditions are considered in the present study-
Finite element model of externally plated RC beam is developed in ABAQUS to study the interfacial stress behaviour in the adhesive layer near the plate end. All the elements are modeled with C3D8R linear brick element. The typical finite element model of the plated beam is shown in the figure 3.
• A uniformly distributed load of 50KN/m is applied along the length of the beam as shown in Figure.2 and the parameters are varied in this loading condition alone. • Two-point loading of 30KN at each point is applied on the beam by maintaining the dimensions of concrete adherent constant and by varying the length of plate, one by terminating plate within the constant moment region and the other by extending plate beyond CMR where bending moment is minimal as shown in figure2. Effect of Adhesive layer thickness Interfacial normal and shear stresses were obtained for four different adhesive layer thicknesses of 1, 2, 3 and 4 mm with all other properties as given in Table.2.Both the interfacial normal and shear stresses are shown in figures 5 and 6 respectively for the region near the plate end.
Finite element model of plated RC beam Poisson’s ratio
Component
Width, mm
Depth, mm
Length, mm
Youngs modulus, MPa
Concrete
130
200
2500
30000
0.2
Adhesive
130
2
1900
2000
0.35
Steel Plate
130
4
1900
200000
0.3
CFRP
130
2
1900
138000
0.21
Effect of adhesive layer thickness on interfacial normal stress
Material properties of adherents in present study
COMPARISONS AND DISCUSSIONS Parametric study A parametric study is presented here in which finite element interfacial normal and shear stress behaviour are compared when one of the parameters was varied each time with all the other values as given in Table 3.3 unless otherwise stated to give a more
Effect of adhesive layer thickness on interfacial shear stress
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International Journal of Research and Innovation (IJRI)
It can be seen that reducing the thickness of the adhesive layer leads to an increase in both the normal stress (figure 4) And the shear stress (figure 5). The peak interfacial normal stress occurs near the end of the plate. At the end of the plate, the interfacial shear stress values are slightly tending towards zero. The peak finite element shear stress occurs at a short distance from the end of the plate, rather than at the end of the plate. Effect of adhesive elastic modulus
Effect of soffit plate thickness on interfacial normal stress
The effect of varying the elastic modulus of the adhesive is shown in figures 6 and 7. As the elastic modulus of the adhesive is increased, the interfacial normal and shear stresses also increase.
Effect of soffit plate thickness on interfacial shear stress
Effect of Soffit plate material
Effect of adhesive elastic modulus on interfacial normal stress
The peak stresses are observed near the plate end and there wasn’t any significant increase in the stress values near the plate and hence adhesive elastic modulus does not show any significance in its consideration for the interfacial stress behavior.
It is very important to investigate and understand the interfacial stress behavior for different types of plates that are used for bending. Hence, carbon fiber reinforced polymer (CFRP) plate is considered due to the rapid growth for it as alternative to steel plate from past few years. An increase in the elastic modulus of the plate leads to an increase in the interfacial stresses. This is easy to understand as a stiff plate takes up a larger share of the total load and this larger share has to be transferred from the beam via higher interfacial stresses. The locations of the peak normal and shear stresses do not vary with the plate elastic modulus.
Effect of adhesive elastic modulus on interfacial shear stress
Effect of Soffit plate thickness An increase in the plate thickness leads to increased interfacial normal stresses. This is as expected, as a larger portion of the total load is resisted by the plate with an increase in thickness. Even though the availability of very thin plates of 1mm and 2mm thicknesses it is considered in the study just to understand how the behaviour of stresses is varying for very thin plates and it is observed that the normal stresses at the plate end for 1mm and 2mm plate are compressive and the peak stresses are formed at a distance little away from the plate end.
Effect of soffit plate material on interfacial normal stress
Effect of soffit plate material on interfacial shear stress
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International Journal of Research and Innovation (IJRI)
Two-point loading condition In practical approaches sometimes plates are terminated within the constant moment region assuming that it will provide the required flexural strength but such practise leads to high interfacial stresses near plate end leading to failure. A huge variation in stresses have been observed near the plate end in the case when plate is restricted with in CMR compared to the other case where plate is extended beyond CMR.
the present study. The present study was focused on the behaviour of interfacial shear and normal stresses in the adhesive layer near the plate end. The parametric study is done when one of the parameters was varied each time with all the other values as given in table 2 unless otherwise stated to give a more comprehensive assessment of the performance of the plated beams when they are subjected to uniformly distributed load. Another loading condition is also considered in the present study i.E. To assess The influence of the position of plate termination on the interfacial stresses under two-point loading. CONCLUSIONS Based on the results of finite element analysis, the following conclusions are derived. [1] In general, it is observed that, uniform stress distributions in the adhesive layer as assumed in early existing approximate analytical solutions are found at a small distance away from the end of the plate.
Effect on interfacial normal stresses
Stress Contours The observation of stress contours helps to understand the interfacial stress behaviour very easily. The most common pattern of the stress contour has been observed in almost all the cases in the present study with the stresses starting high near the plate end and gradually decreasing along the length of plate.
Stress contour of adhesive when plate is terminated in CMR
Stress contour of adhesive layer for beam subjected to UDL
Summary A careful finite element investigation into interfacial stresses in reinforced concrete beams strengthened with a bonded soffit plate has been dealt in
[2] To analyze externally plated rc beams for accurate determination of the interfacial stresses, a very fine mesh has to be used so that the effect of any further mesh refinement is reduced to a zone near the end of the plate. [3] Finite element results showed that stresses vary strongly in the adhesive layer, in particular near the end of the plate. [4] Under the action of uniformly distribute load, the following conclusion are derived from the parametric study. i.The interfacial stresses were found to increase with a reduction in adhesive layer thickness, and peak stress values are obtained near the plate end then the stress distribution is almost uniform a little away from end of the plate. ii.The interfacial stresses were found to increase with an increase in adhesive elastic modulus and plate thickness. iii.The effect of adhesive elastic modulus haven’t shown any significant variation in adhesive stresses whereas, the variation in adhesive thickness have shown significant influence on stress distribution particularly near the plate end. iv. The replacement of cfrp to steel plate has shown a considerable amount of reduction in peak stresses. [5] Under the action of two-point loading i.Termination of plate within the constant moment region is resulting to very strong variation in stresses near the plate end and the peak values are high compared to case of which plate extended beyond cmr. ii.It is found feasible to terminate plate at a position where bending moment is minimal for a better performance of the beam. iii.Further parametric studies in this case and 120
International Journal of Research and Innovation (IJRI)
consideration of shear deformation effect helps for complete assessment of stress distributions. [6] By considering all the above conclusions and existing design a predictive model can be prepared in practical approach which helps for better performance of structure. REFRENCES [1] Tim Stratford, John Cadei (2006) “Elastic analysis of adhesion stresses for the design of a strengthening plate bonded to a beam”, Construction and Building Materials 20 (2006) 34–45.
(2007) “Interfacial shear stress in FRP-plated RC beams under symmetric loads”, Cement & Concrete Composites 29 (2007) 421–432. [12] Mohammed Raoof, Jamal A, El-Rimawi, Mahmoud A.H. Hassanen (1998) “Theoretical and experimental study on externally plated RC Beams”, Engineering Structures 22 (2000) 85–101. AUTHOR
[2]V.Narayanamurthy, J.F.Chen, J.Cairns, A.Ramaswamy (2011) “Effect of shear deformation on interfacial stresses in plated beams subjected to arbitrary loading”, International Journal of Adhesion & Adhesives 31 (2011) 862–874. [3] J.G. Teng, J.W. Zhang, S.T. Smith (2001) “Interfacial stresses in reinforced concrete beams bonded with a soffit plate: a finite element study”, Construction and Building Materials 16(2002).1-4.
T.Haseena, Research Scholar, Department Of Civil Engineering, Aurora Scientific Technological and Research Academy, Hyderabad India.
[4] Abu Thomas Zachariah (2006) “Finite Element Modelling of Adhesive Interface between Steel and CFRP”, Chalmers, Civil and Environmental Engineering, Master’s Thesis 2006:61. [5] S.T. Smith, J.G. Teng (2000) “Interfacial stresses in plated beams”, Engineering Structures 23 (2001) 857–871. [6] Boucif Guenaneche, Abdelouahed Tounsi, El Abbas Adda Bedia (2013) “Effect of shear deformation on interfacial stress analysis in plated beams under arbitrary loading”, International Journal of Adhesion & Adhesives.
Dr. M.V.Seshagiri rao, Professor, Department Of Civil Engineering, JNTU Hyderabad Hyderabad, India
[7] Fangliang Chen, Pizhong Qiao (2009) “Debonding analysis of FRP–concrete interface between two balanced adjacent flexural cracks in plated beams”, International Journal of Solids and Structures 46 (2009) 2618–2628. [8] Deric John Oehlers, John Paul Moran (1990) “Premature failure of externally plated reinforced concrete beams”, Journal of Structural Engineering. 1990.116:978-995.
K. Mythili Associate professor , Department Of Civil Engineering, Aurora Scientific Technological and Research Academy, Hyderabad India.
[9] M. Z. Jumaat, M. A. Rahman, M. A. Alam, M. M. Rahman (2011) “Premature failures in plate bonded strengthened RC beams with an emphasis on premature shear,” International Journal of the Physical Sciences Vol. 6(2), pp. 156-168. [10] V. Narayanamurthy, J.F. Chen, J. Cairns, D.J. Oehlers (2012) “Plate end debonding in the constant bending moment zone of plated beams”, Composites: Part B 43 (2012) 3361–3373. [11] Jian Yang, Jianqiao Ye, Zhongrong Niu 121